Medium Edge Of Hexakis Icosahedron Given Short Edge Calculator

Formula Used:

\[ \text{Medium Edge} = \frac{3}{22} \times (4 + \sqrt{5}) \times \frac{44 \times \text{Short Edge}}{5 \times (7 - \sqrt{5})} \]

Medium Edge of Hexakis Icosahedron:

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1. What is the Medium Edge of Hexakis Icosahedron?

The Medium Edge of Hexakis Icosahedron is the length of the edge that connects two non-adjacent and non-opposite vertices of the Hexakis Icosahedron. It is one of the three distinct edge lengths in this complex polyhedron.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ \text{Medium Edge} = \frac{3}{22} \times (4 + \sqrt{5}) \times \frac{44 \times \text{Short Edge}}{5 \times (7 - \sqrt{5})} \]

This formula establishes the precise mathematical relationship between the medium edge and short edge lengths in a Hexakis Icosahedron.

3. Formula Explanation

The formula incorporates:

Mathematical constants including √5 (approximately 2.23607)
Rational coefficients derived from the geometric properties of the Hexakis Icosahedron
The relationship between different edge lengths in this specific polyhedron

4. Using the Calculator

Instructions: Enter the length of the short edge in meters. The value must be a positive number. The calculator will compute the corresponding medium edge length based on the geometric relationship.

5. Frequently Asked Questions (FAQ)

Q1: What is a Hexakis Icosahedron?
A: A Hexakis Icosahedron is a Catalan solid that is the dual of the truncated dodecahedron. It has 120 faces, 180 edges, and 62 vertices.

Q2: How many different edge lengths does a Hexakis Icosahedron have?
A: A Hexakis Icosahedron has three distinct edge lengths: short, medium, and long edges.

Q3: What are typical applications of this calculation?
A: This calculation is used in geometry, crystallography, architectural design, and 3D modeling where precise polyhedral dimensions are required.

Q4: How accurate is this formula?
A: The formula is mathematically exact and provides precise results based on the geometric properties of the Hexakis Icosahedron.

Q5: Can this calculator handle different units?
A: The calculator uses meters as the default unit, but you can convert your measurements to meters before input, then convert the result back to your desired unit.